where the overline denotes filtering at a scale of \(2\Delta \) , \(z_1\)  is the half vertical grid distance, and \(\tau _{xz}\)  and \(\tau _{yz}\)  are the shear stresses in the streamwise and spanwise directions, respectively. The \(2\Delta \)  filtering was suggested by [1]} to reduce the log-layer mismatch [2]}. The reasoning for this procedure is that the filtering preserves the important large scale variations. At the same time, the use of filtered velocities results in an average stress that is very close to the stress predicted by the average similarity formulation for homogeneous
surfaces [1]}. The vertical derivative at the first horizontal plane is calculated using the Monin-Obukhov similarity
theory without stability correction [4]}, which is implemented following the method proposed by [5]}.
